We investigate the rewrite relation over graphs induced by constructor-based weakly orthogonal graph rewriting systems. It is well known that this relation is not confluent in general whereas it is confluent in the case of weakly orthogonal term rewriting systems. We show, however, that the considered relation is always confluent, as well as confluent modulo bisimilarity, for a large class of g...

The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significant improvements upon the best known asymptotic bounds on the number of admissi...